original text of the thesis:
Population dynamics of the Gyrinid beetle Gyrinus marinus Gyll (Coleoptera)
With special reference to its dispersal activities (1987)

VIII-B. SOME FINAL CONCLUSIONS.

The simulations lead to the following conclusions and hypotheses:

- According to the key-factor analysis population size and its fluctuations are principally determined by survival from hibernation. None of the other processes or stages - either alone or in combination - seem to be able to compensate the high and variable losses from hibernation.

- However, by spreading the risk over a number of habitats it appears to be possible to counterbalance the losses from hibernation in a particular habitat by the differing fluctuations in numbers in other habitats, which are actualized by means of exchange of individuals between the habitats.

- Dispersal, even when it occurs at a low frequency, appears to be crucial for the survival of a species in a group of different habitats. Low frequency dispersal may suffice to prevent extinction of populations and/or lead to refounding at sites where extinction has taken place. Emigration from and immigration into habitats has a strong stabilizing influence on population size, thus decreasing the chance of extinction of the populations considered.

- If dispersal activities are connected with only one recessive genotype the numbers of the 'non-dispersing' genotypes may vary considerably, whereas the fluctuations in numbers of the 'dispersing' genotype are much smaller. The 'dispersing' genotype decreases the chance of extinction for the entire population, also for the heterozygote and homozygote fractions of the population. The relative frequency of the 'dispersing' genotype may become very low as a result of dispersal activities, but the chance that it disappears altogether is small because of the buffering effect of the heterozygote.

- The influence of dispersal activities upon the course of population size depends on the difference between the rates of emigration and immigration, i.e. on survival (s) during dispersal, and on the survival chance (Q) in the habitats. Also of importance will be the variability (v) of the processes that are responsible for the spatial and temporal fluctuations in population size, the number (n) of habitats in the area, and the distances (d) between these habitats. As we saw, it also matters whether dispersal occurs during or out of reproduction (r). Therefore, it may be expected that natural selection will stabilize the level of dispersal (e) of a species in a certain area such that the balance between the risks and the advantages of dispersal activity will be about optimal according to the above definition. These relations can be expressed by the formula:

             F(s).F(v).F(n)
  F(e) = ----------------
             F(Q).F(d).F(r)

where each F(x), if x = s,v,..r, respectively, stands for some function between dispersal activity and the parameter concerned.

- For the field populations of Gyrinus marinus studied the hypothesis cannot be rejected that the flight activities of some of the beetles depend only on favourable weather conditions, even when local conditions are favourable for survival.

- The simulations confirm both the hypothesis of 'spreading of risk' of den Boer (1968, also Reddingius and den Boer 1970) and the effects noticed by Kuno (1981). The simulations make clear that 'Kuno' effects will only occur when offspring migrate between clusters or sites, and much less or not at all when reproducing females change sites. The principal effect of spreading the risk is the significant decrease of the chance of extinction of populations.

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